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Lesson 12 of 17
  • Year 8

Solving complex linear equations

I can solve complex linear equations, including those involving reciprocals.

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Lesson 12 of 17
New
New
  • Year 8

Solving complex linear equations

I can solve complex linear equations, including those involving reciprocals.

Lesson details

Key learning points

  1. Any linear equation written in the form Ax + B = C can be solved.
  2. Equations involving division by a constant can be manipulated to reach the form Ax + B = C.
  3. Equations involving division by a variable can be manipulated to reach the form Ax + B = C.

Keywords

  • Equation - An equation is used to show two expressions that are equal to each other.

Common misconception

Pupils often "multiply through by $$5$$" and turn $${{2x+1}\over5}={10}$$ into $${{10x+5}}={50}$$

Use equivalent fractions as opposed to multiplying through. In one simple step $${{2x+1}\over5}={10}$$ becomes $${{2x+1}\over5}={50\over5}$$


To help you plan your year 8 maths lesson on: Solving complex linear equations, download all teaching resources for free and adapt to suit your pupils' needs...

The key is for pupils to be able to fluently use their fractions skills and knowledge when manipulating algebra. Use a numerical fractions starter to ensure they recall key skills like multiplying a fraction by an integer, and by another fraction.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
$$1\over7$$ is the of $$7$$

fraction
division
Correct answer: reciprocal
divisor
multiplier

Q2.
Solve $$6x+9=27$$

Correct answer: $$x=3$$
$$x=6$$
$$x=9$$
$$x=18$$

Q3.
Solve $${x\over3}=15$$

Correct answer: $$x=45$$
$$x=18$$
$$x=5$$
$$x={1\over5}$$

Q4.
Calculate $${2\over3}\times{4\over5}$$

$$6\over15$$
$$6\over20$$
Correct answer: $$8\over15$$
$$10\over12$$
$$12\over10$$

Q5.
Which of these expressions are equivalent to $${{x+1}\over3}\times{2\over3}$$ ?

$${2x+1}\over9$$
Correct answer: $${2{(x+1)}\over9}$$
$${2{(x+1)}\over3}$$
$${2x+2}\over3$$
Correct answer: $${2x+2}\over9$$

Q6.
Expand and simplify $$8({{x}\over8})$$

$$8$$
Correct answer: $$x$$
$$8x$$
$${{8x}\over8}$$
$$x=8$$

Assessment exit quiz

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6 Questions

Q1.
$${{56}\over{y}}=7$$ is an example of a equation.

variable
Correct answer: rational
irrational
special

Q2.
The solution to $${{6x−2}\over{4}}=7$$ is $$x=$$

Correct Answer: 5, five

Q3.
Solve $${{2x}\over{3}}+1=11$$

Correct answer: $$x=15$$
$$x=16$$
$$x=17$$
$$x=18$$

Q4.
Which is the most efficient first step when solving the equation $${{x+7}\over{9}}={{x-1}\over{3}}$$ ?

Subtract $$7$$ from both sides.
Add $$1$$ to both sides.
Correct answer: Multiply both sides by $$9$$
Multiply both sides by $$3$$
Multiply both sides by $$27$$

Q5.
Solve $${{x+7}\over{9}}={{x−1}\over{3}}$$. The solution is $$x=$$

Correct Answer: 5, five

Q6.
Solve $${{32}\over{3x}}=8$$

$$x={3\over4}$$
$$x=3$$
$$x=4$$
Correct answer: $$x={4\over3}$$